Finite Group Databasebeta

← #14471568

Subgroups — #14471568

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756486C211yesmaximal, characteristic
2#11752487C211yesmaximal, characteristic, complemented
3C5×#5093C211yesmaximal, characteristic, complemented
4C3×#65383C211yesmaximal, characteristic, complemented
5#11747428C212yesmaximal, complemented
6#11747426C212yesmaximal
7#11747305C212yesmaximal, complemented
8#11747279C212yesmaximal
9#11747087C211yesmaximal, characteristic
10C4×#6658C211yesmaximal, characteristic
11#11746855C211yesmaximal, characteristic, complemented
12#10613351—31nomaximal, Hall
13C2×Q8×D15—21no—
14C3×C5×C4⋊Q8C2211yescharacteristic
15#91835—21no—
16#91785—22no—
17#91782C2212yes—
18#91777C2212yes—
19C4×D60C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C5×#869C2211yescharacteristic
22C3×C4×Dic10C2211yescharacteristic
23#91388—21no—
24#91385C2212yes—
25#91344C2212yes—
26#91336—22no—
27#91333—21no—
28C2×#6660C2212yes—
29C2×#6658C2211yescharacteristic
30C5×#810C2212yes—
31C5×#810C2212yes—
32C4×C5×C3⋊C8C2211yescharacteristic
33C3×#3942C2212yes—
34C3×#3940C2212yes—
35C3×C4⋊#168C2211yescharacteristic
36#90987C2211yescharacteristic
37#90983C2212yes—
38#90973C2212yes—
39#90971C2211yescharacteristic
40#90968C2211yescharacteristic
41#90951C2212yes—
42#81037—51nomaximal, Hall
43#66061—31no—
44#66055—31no—
45C5×#487—31no—
46#65383D311yescharacteristic, complemented
47#65372—31no—
48#65107—32no—
49#65081—32no—
50#65080—32no—
51#65077—32no—
52C4×#677—31no—
53C8×Dic10—31no—
54C2×C3×C5×Q8—21no—
55Q8×D15—44no—
56C2×D60C2311yescharacteristic
57C2×C4×D15—21no—
58C2×C4×D15—22no—
59C2×Dic30—22no—
60C2×Dic30D411yescharacteristic
61C2×C5×Dic6C2312yes—
62C2×C3×Dic10C2311yescharacteristic
63C3×C5×C4⋊C4—21no—
64C3×C5×C4⋊C4C2312yes—
65C3×C42×C5C2311yescharacteristic
66#6714—21no—
67#6714—22no—
68C4⋊Dic15D411yescharacteristic
69C4⋊Dic15C2311yescharacteristic
70#6712—22no—
71#6712D412yes—
72C4×Dic15C2312yes—
73C5×C4⋊Dic3—21no—
74C5×C4⋊Dic3—21no—
75C2×C5×C3⋊C8C2311yescharacteristic
76C2×C5×C3⋊C8C2311yescharacteristic
77C3×C4⋊Dic5C2311yescharacteristic
78C3×#683—21no—
79C3×C4×Dic5—21no—
80C2×C3×#168C2312yes—
81Dic3⋊Dic5—22no—
82#6669—22no—
83#6669—22no—
84Dic3×Dic5—22no—
85#6660—24no—
86#6658—22no—
87#5727—51no—
88#5567—51no—
89C3×#475—51no—
90#5093D511yescharacteristic, complemented
91C4×#215—51no—
92#4854—52no—
93#4852—52no—
94#4841—51no—
95#4830—51no—
96#4818—52no—
97#4792—52no—
98C2×Q8×D5—61no—
99C5×C4⋊Q8—31no—
100C5×C4⋊Q8C2×D311yescharacteristic
101#4092—61no—
102Q8×Dic5—32no—
103#4090—32no—
104C2×#688—32no—
105C2×#677—31no—
106#4042—62no—
107#4039—32no—
108#4036—61no—
109#4035—62no—
110#4034—32no—
111#4033—61no—
112C4×D20—31no—
113C4×Dic10—31no—
114C4×Dic10C2×D311yescharacteristic
115C5×#103—32no—
116C5×#103—32no—
117C4×C5×C8—31no—
118#3967—32no—
119#3953—31no—
120#3949—31no—
121#3948—31no—
122#3946—32no—
123C8×Dic5—32no—
124#3942C2×D312yes—
125#3940C2×D312yes—
126C4⋊#168C2×D311yescharacteristic
127#3359—151noSylow
128C22×D15—21no—
129C3×C5×Q8—42no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2411yescharacteristic
134C2×Dic15—21no—
135C2×Dic15C2×D412yes—
136C2×Dic15C2×D412yes—
137D60—21no—
138D60#4112yes—
139C4×D15—42no—
140C4×D15—44no—
141Dic30—44no—
142Dic30SD1614yescomplemented
143C2×C5×Dic3—22no—
144C5×Dic6—22no—
145C5×Dic6—22no—
146C2×C3×Dic5—21no—
147C2×C3×Dic5—21no—
148C3×Dic10—21no—
149C3×Dic10—21no—
150C3×#168—22no—
151C5×C3⋊C8—21no—
152C5×C3⋊C8—21no—
153C2×D3×Q8—101no—
154C3×C4⋊Q8C2×D511yescharacteristic
155C3×C4×Q8—51no—
156#946—101no—
157#944—52no—
158C2×#215—51no—
159C2×#204—52no—
160#896—102no—
161#893—52no—
162#889—102no—
163#888—52no—
164#887—52no—
165C4×D12—51no—
166#870—101no—
167#869C2×D511yescharacteristic
168C4×Dic6—51no—
169C4×Dic6—101no—
170C3×#106—52no—
171C3×C4⋊C8—51no—
172C3×#103—52no—
173#835—51no—
174#816—52no—
175Dic3⋊C8—52no—
176C8×Dic3—52no—
177#810C2×D512yes—
178#810C2×D512yes—
179#809—51no—
180#808—51no—
181C4×C3⋊C8C2×D511yescharacteristic
182C2×C5×Q8—21no—
183C2×C5×Q8—32no—
184Q8×D5—124no—
185C2×D20—31no—
186C2×C4×D5—62no—
187C2×C4×D5—61no—
188C2×Dic10—31no—
189C2×Dic10—62no—
190C2×Dic10C22×D311yescharacteristic
191C2×C5×C8—31no—
192C2×C5×C8—31no—
193C5×C4⋊C4—21no—
194C5×C4⋊C4—61no—
195C5×C4⋊C4—61no—
196C5×C4⋊C4C22×D312yes—
197C42×C5C22×D311yescharacteristic
198#688—64no—
199#685—62no—
200#685—61no—
201C4⋊Dic5—31no—
202C4⋊Dic5—31no—
203C4⋊Dic5—62no—
204C4⋊Dic5C22×D311yescharacteristic
205#683—21no—
206#683—32no—
207#683—62no—
208#683—62no—
209#683—62no—
210C4×Dic5—21no—
211C4×Dic5—32no—
212C4×Dic5—62no—
213C2×#168C22×D312yes—
214#677—62no—
215#557—151no—
216D4×Q8—151no—
217#487—31no—
218#487—152no—
219#475—51no—
220#475—152no—
221#461—152no—
222#461—151no—
223C8×Q8—151no—
224C4×SD16—151no—
225C4×SD16—152no—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—22no—
228C2×D15—41no—
229C2×D15—41no—
230C3×C4×C5—21no—
231C3×C4×C5—42no—
232C3×C4×C5C2×SD1612yes—
233C3×C4×C5C2×#4111yescharacteristic
234C3×C4×C52−1+411yescharacteristic
235Dic15—22no—
236Dic15—41no—
237Dic15C2×SD1614yes—
238C3×Dic5—41no—
239C3×Dic5—41no—
240C5×Dic3—42no—
241C2×C3×Q8—21no—
242C2×C3×Q8—51no—
243D3×Q8—204no—
244C2×D12—51no—
245C2×C4×D3—102no—
246C2×C4×D3—101no—
247C2×Dic6—51no—
248C2×Dic6—102no—
249C2×Dic6C22×D512yes—
250C2×C3×C8—52no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—51no—
253C3×C4⋊C4—101no—
254C3×C4⋊C4C22×D512yes—
255C3×C42—101no—
256C3×C42C22×D511yescharacteristic
257#215—102no—
258(C2×D3)⋊C4—102no—
259(C2×D3)⋊C4—101no—
260C4⋊Dic3—21no—
261C4⋊Dic3—21no—
262C4⋊Dic3—51no—
263C4⋊Dic3—51no—
264Dic3⋊C4—52no—
265Dic3⋊C4—102no—
266Dic3⋊C4—102no—
267Dic3⋊C4—102no—
268Dic3⋊C4—102no—
269C4×Dic3—52no—
270C4×Dic3—102no—
271C2×C3⋊C8C22×D511yescharacteristic
272C2×C3⋊C8C22×D511yescharacteristic
273#204—104no—
274C22×D5—61no—
275C5×Q8—42no—
276C5×Q8—62no—
277C5×Q8—62no—
278C2×C4×C5—22no—
279C2×C4×C5—62no—
280C2×C4×C5D3×D411yescharacteristic
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5C23×D311yescharacteristic
283C2×Dic5—21no—
284C2×Dic5—21no—
285C2×Dic5—32no—
286C2×Dic5—32no—
287C2×Dic5—61no—
288D20—32no—
289D20—61no—
290C4×D5—124no—
291C4×D5—122no—
292Dic10—21no—
293Dic10—21no—
294Dic10—34no—
295Dic10—124no—
296C5×C8—61no—
297C5×C8—61no—
298#168—22no—
299C22×Q8—301no—
300C2×SD16—151no—
301C2×SD16—152no—
302C4⋊Q8—31no—
303C4⋊Q8—152no—
304C4⋊Q8—152no—
305C4⋊Q8D3×D511yescharacteristic
306#125—301no—
307#125—302no—
308C22⋊Q8—302no—
309C22⋊Q8—301no—
310C4×Q8—51no—
311C4×Q8—151no—
312C4×Q8—152no—
313C4×Q8—301no—
314C4×D4—152no—
315C4×D4—151no—
316#106—52no—
317#106—151no—
318C4⋊C8—51no—
319C4⋊C8—152no—
320#103—32no—
321#103—32no—
322#103—52no—
323#103—151no—
324#103—152no—
325#102—151no—
326C4×C8—31no—
327C4×C8—152no—
328C2×C3×C5#54811yescharacteristic
329C2×C3×C5C22×SD1611yescharacteristic
330C2×C3×C5#57811yescharacteristic
331D15—42no—
332C22×D3—101no—
333C3×Q8—42no—
334C3×Q8—101no—
335C3×Q8—101no—
336C2×C3×C4—22no—
337C2×C3×C4—101no—
338C2×C3×C4—101no—
339C2×C3×C4D4×D511yescharacteristic
340C2×C3×C4D4×D511yescharacteristic
341C2×C3×C4C23×D511yescharacteristic
342C2×Dic3—22no—
343C2×Dic3—52no—
344C2×Dic3—52no—
345C2×Dic3—101no—
346D12—52no—
347D12—101no—
348C4×D3—204no—
349C4×D3—202no—
350Dic6—22no—
351Dic6—22no—
352Dic6—54no—
353Dic6—204no—
354C3×C8—102no—
355C3⋊C8—21no—
356C3⋊C8—21no—
357C22×C5C2×D3×D411yescharacteristic
358C2×D5—62no—
359C2×D5—121no—
360C2×D5—121no—
361C4×C5—21no—
362C4×C5—42no—
363C4×C5—122no—
364C4×C5D3×SD1612yes—
365C4×C5#100711yescharacteristic
366C4×C5D3×#4111yescharacteristic
367Dic5—34no—
368Dic5—41no—
369Dic5—41no—
370Dic5—62no—
371Dic5—121no—
372C2×Q8—21no—
373C2×Q8—32no—
374C2×Q8—51no—
375C2×Q8—151no—
376C2×Q8—302no—
377C2×Q8—604no—
378C2×D4—151no—
379C22×C4—302no—
380C22×C4—301no—
381SD16—302no—
382SD16—304no—
383C2×C8—31no—
384C2×C8—31no—
385C2×C8—52no—
386C4⋊C4—21no—
387C4⋊C4—51no—
388C4⋊C4—61no—
389C4⋊C4—61no—
390C4⋊C4—101no—
391C4⋊C4—152no—
392C4⋊C4—151no—
393C4⋊C4—151no—
394C4⋊C4—302no—
395C4⋊C4—302no—
396C4⋊C4—302no—
397C4⋊C4—302no—
398C4⋊C4C2×D3×D512yes—
399C22⋊C4—302no—
400C22⋊C4—301no—
401C42—101no—
402C42—152no—
403C42—302no—
404C42C2×D3×D511yescharacteristic
405C3×C5#335911yescharacteristic, complemented, Hall
406C22×C3C2×D4×D511yescharacteristic
407C2×D3—102no—
408C2×D3—201no—
409C2×D3—201no—
410C3×C4—21no—
411C3×C4—42no—
412C3×C4—201no—
413C3×C4—201no—
414C3×C4D5×SD1612yes—
415C3×C4D5×#4111yescharacteristic
416C3×C4#415011yescharacteristic
417Dic3—42no—
418Dic3—54no—
419Dic3—102no—
420Dic3—201no—
421C2×C5#563311yescharacteristic
422C2×C5C2×D3×SD1611yescharacteristic
423C2×C5#577911yescharacteristic
424D5—122no—
425C23—301no—
426Q8—42no—
427Q8—62no—
428Q8—62no—
429Q8—101no—
430Q8—101no—
431Q8—154no—
432Q8—604no—
433D4—152no—
434D4—301no—
435C2×C4—22no—
436C2×C4—62no—
437C2×C4—101no—
438C2×C4—101no—
439C2×C4—152no—
440C2×C4—152no—
441C2×C4—301no—
442C2×C4—604no—
443C2×C4—602no—
444C2×C4#679011yescharacteristic
445C2×C4#679011yescharacteristic
446C2×C4C22×D3×D511yescharacteristic
447C8—61no—
448C8—61no—
449C8—102no—
450C2×C3#6601111yescharacteristic
451C2×C3C2×D5×SD1611yescharacteristic
452C2×C3#6610011yescharacteristic
453D3—202no—
454C5#8103711yescharacteristic, complemented, Sylow
455C22—302no—
456C22—601no—
457C22—601no—
458C22C2×#679011yescharacteristic
459C4—21no—
460C4—42no—
461C4—122no—
462C4—154no—
463C4—201no—
464C4—201no—
465C4—302no—
466C4—601no—
467C4#9148712yes—
468C4#9203011yescharacteristic
469C4#9203411yescharacteristic
470C3#1061335111yescharacteristic, complemented, Sylow
471C2—602no—
472C2C2×#9148711yescharacteristic
473C2#1175511911yescharacteristic
474C2#1175523811yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×D60C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3359
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #11752487C2semidirect
3. C5×#5093C2semidirect
4. C3×#65383C2semidirect
5. #11747428C2semidirect
7. #11747305C2semidirect
11. #11746855C2semidirect
46. #65383D3semidirect
90. #5093D5semidirect
142. Dic30SD16semidirect
405. C3×C5#3359semidirect
454. C5#81037semidirect
470. C3#10613351semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117564862
#117524872
C5×#50932
C3×#653832
#117474282
#117474262
#117473052
#117472792
#117470872
C4×#66582
#117468552
#106133513
#810375